Phase diagram and structure of the ground state of the antiferromagnetic Ising model on a body-centered cubic lattice

The Monte Carlo method has been used to study phase transitions and the structure of the ground state of the antiferromagnetic Ising model on a body-centered cubic lattice taking into account the interactions of nearest and next nearest neighbors. All possible magnetic structures of the ground state have been obtained for the first time as a function of the ratio of exchange interactions $r$. It is shown that six different orderings in the ground state are possible in the system as a function of the $r$ value. The phase diagram of the dependence of the critical temperature on the interaction of the next nearest neighbors is constructed. For the first time, a narrow region ($2/3<r\leqslant 0.75$) is found in the diagram where the transition from the antiferromagnetic phase to the paramagnetic phase occurs as a first-order phase transition. It is shown that the competition between exchange interactions at the value $r=2/3$ does not lead to the frustration and degeneracy of the ground state.